The solar, longwave, and convective interactions between a window, its shading attachments and its surroundings constitute a complicated coupled heat balance problem that can entail significant computational intensity to simulate in detail. A novel approach represents the fenestration system using several indices of merit – most notably the U-factor and a cross-coupling coefficient. CPU time is reduced without forfeiting features such as the ability to distinguish between air and mean radiant temperatures. The required indices of merit are obtained using thermal network theory and can safely be re-evaluated much less frequently than each time-step, or they can be revised as needed in response to changes in sun angle or shade geometry (e.g., blind slat adjustment). This method has been used to integrate the ASHWAT fenestration model with the California Simulation Engine, a detailed residential model. ASHWAT supports many combinations of glazing and shading layers separated by arbitrary fill gases or by gaps open to outdoor or indoor air. This implementation demonstrates a method that offers generality and detail while providing the input simplicity and computational speed required for practicality.